Well, it's not quite the same thing. I mean, Turkish is finely ground, sure, but it's also served with those fine grounds IN it. The ground size isn't going to make much of a difference if you are actually ingesting the beans.
French presses generally use coarse ground coffee, but it's steeped in the boiling water for five minutes, unlike the drip which just filters down through a medium grind. So even if there's less overall surface area to extract the coffee's oils and caffeine from, there's a great deal more time to do so.
And if you are using a drip press with a paper filter, which I hope you aren't because FLAVOR, it'll further reduce caffeine content. Maybe not by a ton, but the paper filter will absorb the coffee's oils instead of transferring them to the pot, and a fair amount of caffeine will be locked in there with them. Only plus size is that it's better for your cholesterol.
Coffee also contains less caffeine as you increase the roast. Blonde roasts with the most, with dark roasts having had some of it burned out. Americans tend to favor Dark Roasts primarily because of a concerted marketing effort started by (what is now) Starbucks back in the 70s. The artisan coffee market is relatively new--until that point, farmers everywhere were growing completely for quantity, not quality. So Starbucks' marketing decided to roast the hell out of the coffee to give it a unique flavor, and get people to adjust to it so they could offer it as a premium product. That's the same reason French Roast is so dark--the type of coffee trees grown in old French colonies (Robusta) aren't engineered to provide premium flavor, they're designed for output. Heavy roasting is how you make them taste good, and the majority of french coffee supply still comes from those places (and French tastes formed off them).
But in the late 70s, early 80s (iirc), a cache of artisan coffee trees (a variety of arabica known as Mundo Novo iirc) were found in... Colombia? Peru? I don't remember... and the farmer who owned the land realized that they could actually properly produce their beans if grown at a higher altitude than most coffee was grown, which actually meant he could use land that was previously useless to him. What he discovered was that their yield was delicious, and he was able to sell those beans for astronomical costs compared to normal beans.
And thus the artisan coffee market was born.
So, nowadays, if you have really good beans, you should favor a blonde roast. Less-awesome beans, medium roast. You're normal Arabica or (especially) Robusta? Dark roast it is.
#Random history lesson of the day because I love coffee and I love history
Okay, another random history lesson, one of my professors was a top scholar on the French Revolution and she's convinced coffee had a huge role in causing both the revolution and the Terror. The popularity of the French Salon had boomed earlier that century, and their popularity had only spread (to the point where many middle class artisans and even the lower class were frequenting coffeehouses almost as frequently as taverns). These became the headquarters for revolutionary ideas, and were driving forces behind the writers and leaders who eventually began the movement.
And for essentially the entirety of the revolution, all of its leaders were sleeping only a handful of hours a night, but drinking coffee all day long. Quite literally, nearly all revolutionaries were dealing with extensive sleep deprivation all the time, which was probably a huge factor in fueling the national paranoia that gripped France from 1792 through 1794.
So yeah, coffee may have been a huge, and often overlooked, cause one of the bloodiest revolutions in popular memory.
It'll be close, but Romney has the momentum.